In a first polishing step, or in a first half of a super precision polishing, a surface of a glass substrate is polished with a first suspension. The first suspension contains particles and a dispersion agent in which the particles are dispersed. The main ingredient of the particles is silicon dioxide (SiO₂), and the average size (D₅₀) of the particles is equal to or less than 100 nm. The dispersion medium comprises an acid solution the pH of which is equal to or less than 4. In a second polishing step, or in a latter half of the super precision polishing, the surface of the glass substrate is continuously polished with a second suspension. The second suspension contains particles and a dispersion agent in which the particles are dispersed. The main ingredient of the particles is silicon dioxide (SiO₂), and the average size (D₅₀) of the particles is equal to or less than 100 nm. The dispersion medium comprises an alkaline solution the pH of which is equal to or more than 8.5.